Fractal character of the auditory neural spike train

Long-counting-time pulse-number distributions (PNDs) were measured from a broad variety of cat primary auditory fibers using different tone and noise stimuli, counting times T, and number of samples N _T. Whereas short-counting-time PNDs (T approximately 50 ms) manifest the presence of spike pairs (an enhancement of even- over odd-count probabilities), the irregular shapes of the long-counting-time PNDs (T>or approximately=0.1 s) reveal that the underlying sequence of action potentials consists of spike clusters when viewed on a longer time scale. For all units measured, the count variance-to-mean ratio (Fano factor) F(T) varied little over some 90 dB change in the stimulus level. On the other hand, F(T) increased substantially as T and/or N _T were increased, corresponding to the capture of larger and larger spike clusters in the counting time. A relationship is developed between the Fano-time function F(T) and the normalized coincidence rate function, g ( tau ) versus delay time tau . The behavior of the PNDs and the scale invariance implicit in fractional-power-law relationships suggest that the neural events on all primary auditory fibers exhibit fractal behavior for sufficiently large times (sufficiently low frequencies).